{
  "id": "0705.4556",
  "version": "v4",
  "published": "2007-05-31T09:59:52.000Z",
  "updated": "2009-08-20T12:00:23.000Z",
  "title": "Quantization of symplectic vector spaces over finite fields",
  "authors": [
    "Shamgar Gurevich",
    "Ronny Hadani"
  ],
  "comment": "Results obtained: March 2005 (under the direction of Ph.D. advisor Joseph Bernstein, Tel-Aviv, Israel) Keywords: Strong Stone-von Neumann theorem, canonocal Hilbert space, quantization functor, Weil representation",
  "journal": "Journal of Symplectic Geometry, Volume 7, Number 4, 1-28, 2009",
  "categories": [
    "math.RT",
    "math-ph",
    "math.AG",
    "math.MP",
    "math.QA",
    "math.SG",
    "quant-ph"
  ],
  "abstract": "In this paper, we construct a quantization functor, associating a complex vector space H(V) to a finite dimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp(V). The main new technical result is a proof of a stronger form of the Stone-von Neumann property for the Heisenberg group. Our result answers, for the case of the Heisenberg group, a question of Kazhdan about the possible existence of a canonical vector space attached to a coadjoint orbit of a general unipotent group over finite field.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-08-20T12:00:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "finite dimensional symplectic vector space",
      "heisenberg group",
      "complex vector space",
      "stone-von neumann property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 775288,
      "adsabs": "2007arXiv0705.4556G"
    }
  }
}